Uniform Convergence of a Linearly Transformed Particle Method for the Vlasov--Poisson System

Abstract

A particle method with linear transformation of the particle shape functions is studied for the 1d-1v Vlasov--Poisson equation, and a priori error estimates are proven which show that the approximated densities converge in the uniform norm. When compared to standard fixed-shape particle methods, the present approach can be seen as a way to gain one order in the convergence rate of the particle trajectories at the cost of linearly transforming each particle shape. It also allows one to compute strongly convergent densities with particles that overlap in a bounded way.